Provide reasons for the statements

given: < 1 and < 3 are vertical angles.
prove: < 1 ~= < 3

each of these will be used once in the reasoning section.
definition of supplementary angles, definition of a linear pair, substitution, subtraction property of equality, and definition of congruence.

3. Definition of linear pair.

4. Definition of supplementary angles.

5. Substitution.

6. Subtraction property of equality.

7. Definition of congruence.

Step-by-step explanation:

Reason 3:

The angles are supplementary because the angles 1 and 2, 2 and 3 form a linear pair and thus because of the definition of linear pair, they are supplementary angles.

Reason 4:

The sum of angles of 1 and 2, 2 and 3 is equal to 180 because these pair of angles are supplementary angles. Supplementary angles are those angles whose sum is 180 degrees.

Reason 5:

Substitute in place of 180 for the first sum.

So,

Reason 6:

.

Since is on either side of equality, we can subtract it using the subtraction property of equality and thus we get:

Reason 7:

As angle 1 is equal to angle 3, therefore by definition of congruence, these angles are congruent.

So,

The reasons that justify the given statements that proves that are:

Reason 3: Definition of linear angles.

Reason 4: Definition of supplementary angles

Reason 5: Substitution.

Reason 6: Subtraction property of equality

Reason 7: Definition of congruence

Statement 3:

are supplementary

are supplementary

Linear angles on a straight line are supplementary angles. Therefore the reason that justifies statement 3 is: Definition of linear angles.

Statement 4:

The sum of two angles that are supplementary to each other equals 180 degrees. Therefore the reason for statement 4 is: Definition of supplementary angles

Statement 5:

Since and ,

therefore,

substituting for 180 into will give us:

We simply substituted here.

Therefore the reason for statement 5 is: Substitution.

Statement 6:

We have,

Subtract 0 from both sides of the equation

(subtraction property of equality)

Therefore, the reason that justifies statement 6 is: Subtraction property of equality

Statement 7:

Definition of congruence states that if two angles are equal in measure, therefore, they are congruent to each other.

The reason that justifies statement 7 is: Definition of congruence

In summary, the reasons that justify the given statements are:

Reason 3: Definition of linear angles.

Reason 4: Definition of supplementary angles

Reason 5: Substitution.

Reason 6: Subtraction property of equality

Reason 7: Definition of congruence

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5x+2x=49

7x=49

x=7. 35 apples

she would want to sell 10 full-year subscriptions and at least 9 half-year subscriptions to get a total of at least $300. 

i hope this answer you! if you have any further questions or concerns, feel free to ask! : )

step-by-step explanation:

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